Block #344,847

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2014, 1:39:31 PM · Difficulty 10.2010 · 6,460,943 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

a949b7c1eb456073b83b7c5f9bf79fe764cbbae185ca3c74fed4bd7317e06711

View on Chainz ↗

Height

#344,847

Difficulty

10.201042

Transactions

Size

1.24 KB

Version

Bits

0a337780

Nonce

165,447

Timestamp

1/5/2014, 1:39:31 PM

Confirmations

6,460,943

Mined by

⛏️ CaR`~gAL8CJrXce8g7Tksu1uGf13c2xAReWqhicJ

Merkle Root

cae44b27541711c38f45e2f521682800c96fa592f10ebb9d3330279099f93f38

Transactions (2)

Coinbase048d0afc65ba11…60ca0b071983d0

1 in → 28 out9.5800 XPM1015 B

AL8CJrXc…ReWqhicJ APXXNbFp…SppKjmSN AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AebWhrRm…K61Qrkws

cb149ff2dbd20d…8d5a91306d1451

1 in → 1 out9.7700 XPM158 B

ANF2bpUH…8Z1WQvCv

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.240 × 10⁹⁹(100-digit number)

12408470219302150509…89757743099143833599

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.240 × 10⁹⁹(100-digit number)

12408470219302150509…89757743099143833599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.240 × 10⁹⁹(100-digit number)

12408470219302150509…89757743099143833601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.481 × 10⁹⁹(100-digit number)

24816940438604301019…79515486198287667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.481 × 10⁹⁹(100-digit number)

24816940438604301019…79515486198287667201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.963 × 10⁹⁹(100-digit number)

49633880877208602038…59030972396575334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.963 × 10⁹⁹(100-digit number)

49633880877208602038…59030972396575334401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

9.926 × 10⁹⁹(100-digit number)

99267761754417204076…18061944793150668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.926 × 10⁹⁹(100-digit number)

99267761754417204076…18061944793150668801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.985 × 10¹⁰⁰(101-digit number)

19853552350883440815…36123889586301337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.985 × 10¹⁰⁰(101-digit number)

19853552350883440815…36123889586301337601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer